A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2021 Jun 23, 08:54 -0700
Robin, you wrote:
"There is another important point that Cook makes but that Williams did not take account of and in fact rejects in his rebuttal. The 1/4 probability is an average over all possible outcomes and does not apply to any one trial. It is relevant before any sights are made but is no longer applicable when the actual realized cocked hat that has been plotted. Once a particular round of sights have been taken the probability that the true position falls in any specific region either inside or outside of the cocked hat depends on the actual distribution of errors. To see this suppose that by dumb luck the sights produce a miniscule cocked hat. The chances that the true position falls inside will be much less than 1/4."
A giant, decidedly non-miniscule yes on that.